The grilling included being asked what Magna Carta meant and who composed Rule Britannia.

The Prime Minister fluffed both questions, but his fellow Old Etonian and Oxford University contemporary Mr Johnson today claimed Mr Cameron really knew Magna Carta meant Great Charter and faked the apparent knowledge gap to appear more down-to-earth.

Classics scholar Mr Johnson said: "I think he was only pretending. I think he knew full well what Magna Carta means.

"It was a brilliant move in order to show his demotic credentials and that he didn't have Latin bursting out of every orifice."

Quizzed on more modern British history during an appearance on LBC 97.3 radio, Mr Johnson failed to correctly identify Geoff Hurst as the scorer of a hat-trick in the 1966 World Cup final victory over West Germany, the only time England have ever been world champions.

Mr Johnson claimed defender Bobby Moore netted three. In fact, Moore was the captain who held aloft the Jules Rimet trophy at Wembley.

Perhaps realising the revelation could damage his dreams of claiming the keys to No 10 Downing Street, the 48-year-old mayor protested: "I was only two!"

In a wide-ranging interview and phone-in with presenter Nick Ferrari, Mr Johnson faced the anger of London taxi drivers frustrated by transport arrangements during the Olympics.

He apologised to businesses whose trade was hit by the summer spectacle, but denied claims the capital became a "ghost town".

Mr Johnson said: "I'm not going to pretend it was a bonanza for everybody and for those that feel hard done by, I'm sorry for the losses or low takings they had.

"But the overall economic benefit to London of people around the world seeing a city that can deliver an amazing event like that so successfully was incredibly positive."

The mayor admitted trade was "patchy", but claimed the Games were "overwhelmingly for the benefit of the city".

He added: "If you look at the spend by tourists in the city, it was up overall.

"The economic impact of the Games is estimated to be massively positive."

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David Cameron on David Letterman

David Cameron on David Letterman

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David Cameron on "The Late Show with David Letterman" - New York

Prime Minister David Cameron (left) talks with talk show host David Letterman on the David Letterman Show in New York, after he addressed the United Nations General Assembly.